Harnessing the Power of Geometric Truth

On Thursday, it was official: George Walker and Jim Tolpin handed over to Lost Art Press all the text and illustrations for their next book, “Euclid’s Door,” and I’ve just begun the initial edit. The book is about ancient layout tools, and what they can teach us…as George’s introduction below tells us. The book – which features illustrations by Barb Walker and Keith Mitchell – will be out later this year.
– Fitz

Belly Hill is a hump in the sprawling wheat fields in southern Turkey. It kept its secrets hidden except in the spring when local farmers snagged their plows on blocks of limestone beneath the soil. Then in 1996 a group of German archeologists took a closer look. What they found turned human history on its head. They unearthed a temple complex known today as Gobekli Tepe, a massive 12,000-year-old building site sprawling across 22 acres, much of it still unexplored.

Scores of giant rectangular stone columns, some more than 20’ high arranged in circles, ovals and triangles. Much of the stonework is decorated with elaborate carvings of spiders, snakes and lions. Stuff that must have haunted the dreams of those early builders. Scholars debate who made those carvings and what they reveal about the builders. The most amazing thing is the early date. The complex goes back 12 millennia. Humans weren’t thought to have built things on this grand scale that far back. This was long before the invention of writing, before pottery, even before the invention of agriculture.  It was built by a hunter-gatherer culture. That wasn’t supposed to happen. It was previously thought that nomadic hunters lived so close to the edge that they didn’t have resources to devote to architecture. So much for that theory. 

When Jim Tolpin and I first read about the dig, we didn’t marvel at the elaborate carvings of snakes and spiders; we noted these builders had a working knowledge of artisan geometry. They understood plumb and level and were able to fabricate large stones with precise flat surfaces and right angles. They obviously possessed a skill-set and tool set that gave them tremendous creative power .

Over the last 10 years we’ve explored how artisans harnessed the truths of geometry throughout history. We began close to home, looking at early American furniture and quickly moved back in time to the Renaissance in Europe. From there, a clear path took us back to ancient Rome, Greece and Egypt, with a few side trips into Asia. Now we find the same thread ties back to prehistoric builders. Yet the structures on the Gobekli Tepe are so developed and refined, it implies that the knowledge about artisan geometry goes way back, deep back.

Tools of the Imagination
Just what was their tool set? Given the scale and complexity of the work, it’s hard to imagine that these early builders spitballed this into existence without the aid of layout and design tools. Flint cutting tools and stone hammers survived, but any tools made of wood or fiber are long gone. No doubt they could have used strings to mark layouts and rough cuts on slabs of stone. A string with a weight attached could also gauge level and plumb. But those smooth flat surfaces and sharp right angles cry out for a sophisticated tool kit to tackle those problems. How did they make a stone (or board) flat and free from twist? How did they execute a corner so they could butt two stones (or boards) together and marry together perfectly?

Most woodworkers are curious about tool marks left behind. It might be the slashes left by an axe on timbers in an old barn or the stray cuts left from a backsaw. We can’t help ourselves. We pull out drawers and look closely at dovetails or crawl under a table to feel the wavy surface left by a scrub plane. Cutting tools leave their distinctive footprints, and another family of tools in the builders’ kit leave their marks hidden in plain sight. An axe or gouge leaves a texture we can see and feel, but some tools leave behind their shadows hidden in plain sight, evidence of artisan geometry at work. Boards that are flat and free of twist with square edges so they can be joined together are a different sort of signature. They are the ghosts artisan geometry left behind and they hint at the tools that created those ghosts. Some of these tools create layout lines that are later erased by a handplane or covered when joinery is knocked together tight and solid. We don’t often think of these ghosts as tool marks, but they speak to us about a set of tools used from ancient times.

In fact, you could divide tool marks and their tools into two categories. One group is for shaping and forming. They leave the marks we can feel with our fingertips. A second group are tools of the imagination that we use to help us with design and layout. They leave a picture of artisan geometry at play. Both sets of tools have something in common. They both flow from the wellspring of artisan geometry, a deep understanding of points, lines and simple shapes. For as long as humans have been building, they have used tools to connect with the universal truths of Geometry. Tools not only help us to cut, smooth and manipulate wood and stone, they help us to harness geometry to create order from chaos. Tools were not just an extension of our hands, they were the means to extend the truths of geometry into the built world.

Ex Nihilo
We can guess about how early humans made technological leaps. It’s not a stretch to think that fires ignited by lightning gave our ancestors a familiarity with fire and the possibilities it offered. A round stone rolling down a hill may have led to the idea of the wheel. Yet how would early humans have stumbled onto the mysteries and possibilities offered by straight lines and right angles? It even seems a larger leap to fabricate tools that could harness these mysteries. Perhaps an account of this will never be understood, but the evidence left by these early builders leaves no doubt that they understood artisan geometry.

These tools that harness the power of geometry generate and prove a handful of geometric truths or axioms, i.e. a straight line is the shortest distance between two points. Yet, long before humans wrote these truths down, they harnessed the power of straight lines, parallel lines, right angles and a number of common angles, such as 45° miters. The one common thing about all these geometric truths is that they are all self-proving. A straight edge can prove itself, a try square or a miter square can prove itself. Just to be clear, every project in this book has a section where we prove the tool. This differs from the geometry you learned in junior high where proofs were expressed as theorems you had to memorize. Although all of the proofs we use could be expressed with theorems, that’s not what we are after. Every proof we use is a physical confirmation we can see or feel. Forget about numbers, they just get in the way. This self-proving property of geometric truths allows them to be created ex nihilo (out of nothing) and this is what we harness in this book to create our elegant set of design and layout tools.

Like the discovery of fire, some inquisitive ancestor of ours may have fussed about with a couple of straight sticks, trying to get them to fit tightly together. Slowly the realization came that the pair of sticks could be used to correct each other. Shave a tiny bit of material from one and it points out the imperfection in the other. Finally they reach an almost magical level of perfect straightness. Then these sticks could become tools that could be used to impart straightness (and flat surfaces) to stones and logs. Our ancestors could have become familiar with these tools of geometry because like the lightning generating fire, the truths of geometry were right at their fingertips. They just needed to become familiar with them, then begin to harness them.

Even though this knowledge goes back into the depths of time, the truths of geometry are still valid, and mastery of geometry is still powerful and brimming with possibilities. In this book we are going to walk in the footsteps of our ancestors both distant and near. We’ll be exploring artisan geometry with sharp tools. Plenty of knife lines and saw cuts. You’ll see the truths of geometry in three dimensions on your workbench – a much better way to grasp these secrets of our craft. We walk through the building of a set of layout tools found in a typical cabinetmaker’s tool chest. Tools that were frequently user made. Jim and I began making these tools ourselves out of curiosity. We came to realize that the process of making these tools results in much more than the tools themselves (which are in fact quite amazing). Today we think of these tools as teachers that take us on a journey into the secrets of artisan geometry.  They develop skills important to the craft. These builds equip both the imagination and the hands.